Customer Reviews

Triangle of Thought

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The goal of this book is "to enable a broad but enlightened audience to bridge the growing gap between the subtleties of these advances (meaning quantum mechanics, relativity and Gödel's theorem), usually accessible only to specialists, and the often unbelievably deformed images of them presented by popularized accounts".

I must disagree. Although the reader will attend an interesting dialogue between some of the top minds of the XXth century and Alain Connes is one of the greatest living mathematicians, it is difficult to follow a great part of this conversation if you are not familiar with advanced mathematics and physics. The publisher could have made the reading easier by including a lot of sidebars as Scientific American does. On the other hand I have read quite a number of books by very good scientists on the topics mentioned (therefore they could not be deformed images) and these books are much more accessible than "Triangle of Thoughts". If you have read the other Connes co-authored book, "Conversations on Mind, Matter and Mathematics", the level of accessibility of this one is similar.

That said, the book is worth reading and there are sections which are quite readable like that on Cosmology, on game theory or even on Gödel's theorem. Alain Connes introduces a distinction between primordial mathematics and axiomatic mathematics which he considers an (limited) instrument of comprehension at our disposal. Gödel affirms that any sufficiently rich axiomatic system contains truths that are not provable and it has the curious consequence that you can add a countertruth to an axiomatic system which will be free of contradiction if the former system was non contradictory.

That the book needs some editing is clear. On one hand the authors describe what a well ordering is, something that is explained in Europe in the first year of college mathematics, on the other the paragraphs such as: "The phase space is sympletic and the Hamiltonian is a function on this space that we call the `energy', and it generates the evolution of observable quantities with its Poisson bracket" give an idea of what the authors understand as "enlightened audience".
In conclusion, the book deserves 5 stars if you are part of such audience, but only three if you are a mere mortal with a good science education.